# Spline

Cubic interpolating plane curve or space curve

• Library:
• Simscape / Multibody / Curves and Surfaces

## Description

This Spline block creates a continuous spline curve based on cubic interpolation between the specified points. The curve can be two dimensional, such as a planar cam profile, or three dimensional, such as a roller coaster track. The dimension of the spline depends on the dimension of the coordinate matrix. An N-by-2 matrix specifies a 2-D curve in the xy plane. An N-by-3 matrix specifies a 3-D curve. All the coordinates are resolved in the local reference frame of the block. Moreover, according to the specified end conditions, the curve can be either open or closed.

## Ports

### Frame

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Spline curve reference frame. Connect this frame port to another block to specify the location and orientation of the spline curve in a model.

### Geometry

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Geometry data associated with the representation of a 2-D or 3-D continuous spline curve. It provides the spline curve specification to other blocks to which it connects, such as the Point on Curve Constraint block.

## Parameters

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Matrix that includes the coordinates of the interpolation points for defining the spline curve. Use an N-by-2 matrix to specify a 2-D spline and an N-by-2 matrix to specify a 3-D spline. Each row of the matrix specifies the Cartesian coordinates of an interpolation point with respect to the reference frame of the Spline block. An error occurs if the matrix has any repeated rows.

#### Tips

You can use the `unique` function to remove repeated rows from an input matrix.

End conditions of the spline curve. The ```Periodic (Closed)``` end conditions correspond to a closed curve. For this condition, the block joins the first and last data points with a continuous curve. The `Natural (Open)` end condition corresponds to an open curve.

The spline curve is a piecewise function of third-order polynomial segments connected end-to-end. The curve is built such that adjacent polynomial segments have the same first and second derivatives at the shared endpoints.

Graphic

Visualization setting for this spline. Use the default setting, `From Geometry`, to show the spline. Select `Marker` to show a graphic marker such as a sphere or frame. Select `None` to disable visualization for this spline.

Parameterizations for specifying visual properties. Select `Simple` to specify diffuse color and opacity. Select `Advanced` to specify more visual properties, such as Specular Color, Ambient Color, Emissive Color, and Shininess.

#### Dependencies

To enable this parameter, set Type to ```From Geometry``` or `Marker`.

True color under direct white light, specified as an [R,G,B] or [R,G,B,A] vector on a 0–1 scale. An optional fourth element specifies the color opacity on a scale of 0–1. Omitting the opacity element is equivalent to specifying a value of 1.

#### Dependencies

To enable this parameter, set Type to `From Geometry` or `Marker`.

Graphic opacity, specified as a scalar in the range of 0 to 1. A scalar of 0 corresponds to completely transparent, and a scalar of 1 corresponds to completely opaque.

#### Dependencies

To enable this parameter, set:

1. Type to `Marker`

2. Visual Properties to `Simple`

Color of specular highlights, specified as an [R,G,B] or [R,G,B,A] vector on a 0–1 scale. The optional fourth element specifies the color opacity. Omitting the opacity element is equivalent to specifying a value of 1.

#### Dependencies

To enable this parameter, set:

1. Type to `From Geometry` or `Marker`

2. Visual Properties to `Advanced`

Color of shadow areas in diffuse ambient light, specified as an [R,G,B] or [R,G,B,A] vector on a 0–1 scale. The optional fourth element specifies the color opacity. Omitting the opacity element is equivalent to specifying a value of 1.

#### Dependencies

To enable this parameter, set:

1. Type to `From Geometry` or `Marker`

2. Visual Properties to `Advanced`

Graphic color due to self illumination, specified as an [R,G,B] or [R,G,B,A] vector on a 0–1 scale. The optional fourth element (A) specifies the color opacity. Omitting the opacity element is equivalent to specifying a value of 1.

#### Dependencies

To enable this parameter, set:

1. Type to `From Geometry` or `Marker`

2. Visual Properties to `Advanced`

Sharpness of specular light reflections, specified as a scalar number on a 0–128 scale. Increase the shininess value for smaller but sharper highlights. Decrease the value for larger but smoother highlights.

#### Dependencies

To enable this parameter, set:

1. Type to `From Geometry` or `Marker`

2. Visual Properties to `Advanced`

Geometrical shape of the graphic marker. The Mechanics Explorer shows the marker using the selected shape.

#### Dependencies

To enable this parameter, set Type to `Marker`.

Size of marker for visualization. The maker size does not scale with zoom level.

#### Dependencies

To enable this parameter, set Type to `Marker`.